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A357854
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Squarefree numbers with a divisor having the same sum of prime indices as their quotient.
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25
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1, 30, 70, 154, 165, 210, 273, 286, 390, 442, 462, 561, 595, 646, 714, 741, 858, 874, 910, 1045, 1155, 1173, 1254, 1326, 1330, 1334, 1495, 1653, 1771, 1794, 1798, 1870, 1938, 2139, 2145, 2294, 2415, 2465, 2470, 2530, 2622, 2639, 2730, 2926, 2945, 2958, 3034
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OFFSET
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1,2
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COMMENTS
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A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
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LINKS
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EXAMPLE
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The terms together with their prime indices begin:
1: {}
30: {1,2,3}
70: {1,3,4}
154: {1,4,5}
165: {2,3,5}
210: {1,2,3,4}
273: {2,4,6}
286: {1,5,6}
390: {1,2,3,6}
For example, 210 has factorization 14*15, and both factors have the same sum of prime indices 5, so 210 is in the sequence.
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MATHEMATICA
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sumprix[n_]:=Total[Cases[FactorInteger[n], {p_, k_}:>k*PrimePi[p]]];
Select[Range[1000], SquareFreeQ[#]&&MemberQ[sumprix/@Divisors[#], sumprix[#]/2]&]
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CROSSREFS
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The partitions with these Heinz numbers are counted by A237258.
Squarefree positions of nonzero terms in A357879.
Cf. A033879, A033880, A064914, A181819, A235130, A237194, A276107, A300273, A321144, A357975, A357976.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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